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Amazon’s mobile store, the suit states, introduced the ability to bill customers within an application — so-called in-app charges — in November 2011, and did so without parental notifications or password requirements in children’s games.

In a letter dated July 1 and addressed to Edith Ramirez, the F.T.C. chairwoman, Andrew DeVore, associate general counsel of Amazon, criticized the agency’s “unwillingness to depart from the precedent it set with Apple.”